Analysis of the effects of stent-induced deformation on the hemodynamics of MCA aneurysms

The use of a stent to coil an aneurysm can alter the position of the main blood vessel and affect blood flow within the sac. This study thoroughly examines the impact of stent-induced changes on the risk of MCA aneurysm rupture. The research aims to assess the effects of coiling and vessel deformation on blood flow dynamics by comparing the OSI, WSS, and blood structure of two distinct MCA aneurysms to identify high-risk areas for hemorrhage. Computational fluid dynamics is used to model blood flow. The results indicate that aneurysm deformation does not always decrease the risk of rupture, and coiling is more effective in occluding blood flow than aneurysm deformation.

www.nature.com/scientificreports/ The simulation of blood hemodynamics inside the MCA aneurysm with/without deformation by stent is done via computational fluid dynamics [29][30][31][32] . The transient form of Navier-stokes is used for the modeling of blood flow through the vessel and sac section [33][34][35] . The one-way FSI model is used to apply the impacts of the vessel interaction under the impacts of blood pressure [36][37][38][39] . This technique is extensively used for the simulation of deformable domain where fluid has impacts on the solid wall [40][41][42] . Computational technique has been used in different applications of engineering 43,44 and medical devices 45,46 . In this approach, the pressure force on the vessel would result in the defamation of the sac and vessel. The bloodstream is assumed transient with cardiac cycle and non-Newtonian 28 . Casson model is applied for the calculation of the blood viscosity 29 .
The geometries of the selected MCA aneurysms are displayed in Fig. 1. The details of the aneurysm characteristics (i.e. sac volume, sac ostium section area, sac neck vessel angle, and …) are also presented in Fig. 1. The geometries of the chosen MCA aneurysms are obtained from aneurisk website which is related to Emory University 28 . This figure also demonstrates the applied boundary condition for the chosen aneurysms. Inflow blood is applied by mass flow rate pattern (Fig. 2a) while outflow is a pressure outlet with a specific profile (Fig. 2b). This study reports the data associated with the 3rd cardiac cycle. The OSI index is calculated at the end of the third cardiac cycle. The hemodynamic results of the four stages (specified in Fig. 2) are presented and compared. Table 1 presents the mass flow rate of these stages. Since the maximum blood flow rate happens at stage b (peak systolic), the contour of pressure and WSS of this stage are presented 29 . Figure 3 illustrated the produced grid for the selected cases with a close-up view. In a close-up view, the quality of produced grids is shown. In the produced grids, the size of the grid near the vessel wall is less than the center of the vessel since the main hemodynamic factors of WSS and OSI are calculated at the wall. In this figure, the sac section is separated for applying the coiling. A grid study is also done to investigate the mesh effects on our results. Table 2 presents the details of four produced grids and their effects on run time and average WSS on sac surfaces for two selected models. Grid analysis indicates that the model with 298201 cells and 402161 cells are appropriate grids for case A and case B, respectively. www.nature.com/scientificreports/ The technique of endovascular coiling is implemented by filling the sac area with uniform porosity. Hence, the permeability of this domain is calculated via the capillary theory of kozeny 29,31 . Details of applied porosity for the selected MCA aneurysms are presented in Table 3. The present work investigated the impacts of two coiling porosities on the hemodynamic of the blood stream. The length and diameter of Coil are 30 cm and 0.254 mm, respectively.     Figure 5 illustrates the contour of the WSS on the sac wall for two coiling porosities of 0.75 and 0.5 for the selected aneurysm (case A) with/without stent deformation. The distribution of the WSS on the sac surface at peak systolic confirms that the influence of deformation on the distribution of WSS without fillings is not noticeable. As the coiling porosity is applied in the sac domain, the region with high WSS is restricted in the neck area where the flow rate of the blood is more than in other sections. In addition, the deformation impacts are more visible on  www.nature.com/scientificreports/ models with lower porosity. In Fig. 6, the effects of aneurysm deformation on the WSS of the sac wall for case B are presented. The results indicate that deformation in this case has great impacts on the location and size of critical regions with high WSS on the sac surface. The impacts of the coiling porosity are substantial when the aneurysm deformation is done. The blood flow diverts efficiently in this case and this reduces the WSS on the sac surface.   www.nature.com/scientificreports/ The pressure contour for the aneurysm (case A) under the impacts of deformation and coiling is displayed in Fig. 7. The effects of aneurysm deformation of the pressure contour show that the deformations greatly reduce the pressure on the sac wall. Meanwhile, the porosity effects on the pressure distribution are not substantial as shown in the figure. In Fig. 8, the impacts of deformation and coiling on the pressure distribution of the MCA aneurysm (case B) are demonstrated. As mentioned before, the defamation of an aneurysm in this case efficiently occluded blood flow into the sac and this reduces the pressure value on the sac wall.  www.nature.com/scientificreports/ To understand the role of deformation on the hemodynamic of the MCA aneurysm, Fig. 9 displays the structure of the blood flow by iso-velocity surfaces in different porosities of coiling. In the original model (without deformation), deformation of the parent vessel does not change the blood feature. As the coiling porosity applied in the sac area, the velocity of blood decreases inside the domain and this reduces WSS on the sac wall. The blood feature of the case B under impacts of coiling and deformation shows how the flow diversion could protect the sac from rupture (Fig. 10). Since the blood entrance into the sac area is limited by deformation, the impacts of coiling porosity is not visible in different coiling porosities.

Results and discussion
OSI index is critical for the evaluation of the aneurysm rupture. Figure 11 demonstrates the contour of OSI at end of the cardiac cycle for an MCA aneurysm (Case A) when aneurysm deformation happens. In the original case (without coiling treatment), the value of OSI does not change meaningfully even after 2nd deformation and the critical region remains at the dome of the aneurysm. This pattern is preserved for cases with coil fillings. The blood entrance does not change due to the deformation of the parent vessel. Figure 12 illustrates the contour of  www.nature.com/scientificreports/ the OSI at end of the cardiac cycle after deformations with/without coiling (Case B). It seems that the OSI index increases after 1st deformation while a substantial decrease is noticed after 2nd deformation.
The results of mean OSI on sac wall for different coiling porosities under impacts of deformations are presented in Fig. 13. In both cases (A and B), the value of the OSI index substantially decreases by coiling rather than deformations. This is due to the role of coiling occlusion which reduces blood shear near the aneurysm wall. In the case of B, the effects of 1Ststage of deformation are not favorable as mentioned in the hemodynamic analysis.

Results and discussion
The impacts of stent-induced deformation on the hemodynamics of two distinctive MCA aneurysms are fully investigated in the present research. This study examined and explored the role of endovascular coiling when the parent vessel is deformed by the implementation of stents on the parent vessel near the sac. The modeling of the bloodstream in vessels and aneurysms is done via the computational fluid dynamic technique. The blood flow feature and WSS of aneurysm are compared to disclose the influence of coiling after post-interventional deformation. Presented results show that the effects of MCA aneurysm deformation are not always favourable for occlusion of the blood entrance. A comparison of coiling and deformations indicate that the coiling of an aneurysm would effectively reduce the risk of MCA aneurysm rupture.  www.nature.com/scientificreports/

Data availability
All data generated or analysed during this study are included in this published article.